While quantifying intrinsic dimension using linear technique such as PCA is standard, estimating the dimension of real-world time series datasets using autoencoders is more challenging. For example, Wang, Yao, and Zhao[1]} used an autoencoder with varying number of nodes in hidden layer MNIST and Olivetti[2]} dataset to determine intrinsic dimension. The authors find that as the number of nodes in hidden layer increased, the classification accuracy increased before plateauing. Our approach is fundamentally different. First, we do not change the network architecture (number of hidden nodes), since we found that using a binary search method to estimate the number of nodes required in hidden layer was quite inefficient. Second, in our approach each class of digits in the MNIST dataset has a different dimension and we have no reason to conjecture that the number of class labels (10 for MNIST) should be the same as intrinsic dimension of each digit.
